Diffusivity self- and transport

To establish the relationship between self- and transport diffusion it is necessary first to consider diffusion in a binary adsorbed phase within a micropore. This can be conveniently modeled using the generalized Maxwell-Stefan approach [45,46], in which the driving force is assumed to be the gradient of chemical potential with transport resistance arising from the combined effects of molecular friction with the pore walls and collisions between the diffusing molecules. Starting from the basic form of the Maxwell-Stefan equation ... 

As an example, see Skoulidas et al. [2]. They reported atomistic simulations for both self- and transport diffusivities of light gases in carbon nanotubes and compared them with transport rates in zeolites with comparable pore sizes. 

The diffusional behavior of p-xylene is complicated. The FR measurements reveal two different diffusivities corresponding to movement through the straight and sinusoidal channels. The ZLC method increases only the average diffusivity which is similar to the value for benzene but it is possible that the difference between the self and transport diffusivity results from the two channel behavior revealed by the FR data [33],... 

Behr W, Haase A, Reichenauer G et al (1998) Self and transport diffusion of fluids in Si02 alcogels studied by NMR pulsed gradient spin echo and NMR imaging. Journal of Non-Crystalline Solids 225 91-95... 

Jobic H, Karger J, Bee M. Simultaneous measurement of self-and transport diffusivities in zeofites. Phys Rev Lett 1999 82 4260-3. 

Diffusivities are often measured under conditions which are far from those of catalytic reactions. Moreover, corresponding to their different nature, the various measuring techniques are limited to special ranges of application. The possibility of a mutual transformation of the various diffusivities would therefore be of substantial practical relevance. Since each of the coefficients of self-diffusion and transport diffusion in single-component and multicomponent systems refers to a particular physical situation, one cannot expect that the multitude of information contained in this set of parameters can in general be adequately reflected by a smaller set of parameters. Any correlation which might be used in order to reduce the number of free parameters must be based on certain model assumptions. 

The expressions derived above, in particular Eqs. 17 and 21, allow one to derive self- or transport diffusivities in a straightforward manner, since the width has a simple DQ law. This Fickian diffusion is only observed at large distances, corresponding to small Q values. Typically, in a molecular Uquid, Fickian diffusion is observed for distances larger than 10 A. For a molecule diffusing in a zeolite, one has to probe translation over a few unit cells (pa 60 A). At smaller distances (larger Q values), there is usually a deviation from the linear relation between Aa> and Q. This sort of deviation is quite general and is due to the details of the elementary diffusive steps. 

Fundamentals of sorption and sorption kinetics by zeohtes are described and analyzed in the first Chapter which was written by D. M. Ruthven. It includes the treatment of the sorption equilibrium in microporous sohds as described by basic laws as well as the discussion of appropriate models such as the Ideal Langmuir Model for mono- and multi-component systems, the Dual-Site Langmuir Model, the Unilan and Toth Model, and the Simphfied Statistical Model. Similarly, the Gibbs Adsorption Isotherm, the Dubinin-Polanyi Theory, and the Ideal Adsorbed Solution Theory are discussed. With respect to sorption kinetics, the cases of self-diffusion and transport diffusion are discriminated, their relationship is analyzed and, in this context, the Maxwell-Stefan Model discussed. Finally, basic aspects of measurements of micropore diffusion both under equilibrium and non-equilibrium conditions are elucidated. The important role of micropore diffusion in separation and catalytic processes is illustrated. 

Transport equations of electrolyte and single ion conductance, self- and mutual-diffusion, and transference numbers can be obtained either from Onsager s orntinuity equation or from Onsager s fundamental equations of irreversible processes. Many publications deal with this matter, especially with electrolyte conductance. For monographs, review articles, surveys of results and recent contributions in this field see Refs. Recent extamons of in-... 

Using this relation, it is possible to compare self-diffusion coefficients and transport diffusivities measured or calculated under equilibrium or... 

A. I. Skoulidas, D. S. ShoU, Self-diffusion and transport diffusion of light gases in metal-organic framework materials assessed using molecular dynamics simulations, J. Phys. Chem. B., 109, 15760-15768 (2005). 

Skoulidas, A. I. Shell, D. S. (2005). Self-Diffusion and Transport Diffusion of Light Gases in Metal-Organic Framework Materials Assessed Using Molecular Dynamics Simulations. r/teJourua/ofP/ sica/C/jemA/ryB, 109(33), 15760-15768. 

Most kinetic growth processes produce objects with self-similar fractal properties, i.e., they look self-similar under transformation of scale such as changing the magnification of a microscope [122]. According to a review by Meakin [134], the origin of this dilational symmetry may be traced to three key elements describing the growth process I) the reactants (either monomers or clusters), 2) their trajectories (Brownian or ballistic), and 3) the relative rates of reaction and transport (diffusion or reaction-limited conditions). The effects of these elements on structure are illustrated by the computer-simulated structures shown in the 3x2 matrix in Fig. 55. 

For the light molecules He and H2 at low temperatures (below about 50°C.) the classical theory of transport phenomena cannot be applied because of the importance of quantum effects. The Chapman-Enskog theory has been extended to take into account quantum effects independently by Uehling and Uhlenbeck (Ul, U2) and by Massey and Mohr (M7). The theory for mixtures was developed by Hellund and Uehling (H3). It is possible to distinguish between two kinds of quantum effects— diffraction effects and statistics effects the latter are not important until one reaches temperatures below about 1°K. Recently Cohen, Offerhaus, and de Boer (C4) made calculations of the self-diffusion, binary-diffusion, and thermal-diffusion coefficients of the isotopes of helium. As yet no experimental measurements of these properties are available. 

Figure 2. Computed transport diffusivities, D, for Xe in AIP04-31 at T = 100, 200, and 300 K. The data is normalized by the T-dependent infinite dilution self-diffusivity,. Do-...

The methods described so far for studying self-diffusion are essentially based on an observation of the diffusion paths, i.e. on the application of Einstein s relation (eq 3). Alternatively, molecular self-diffusion may also be studied on the basis of the Fick s laws by using iso-topically labeled molecules. As in the case of transport diffusion, the diffusivities are determined by comparing the measured curves of tracer exchange between the porous medium and the surroundings with the corresponding theoretical expressions. As a basic assumption of the isotopic tracer technique for studying self-diffusion, the isotopic forms are expected to have... 

---